Q. 24

# Show that a diagonal divides a parallelogram into two triangles of equal area.

Answer :

Given: A parallelogram ABCD with a diagonal BD

To prove: area(∆ABD) = area(∆BCD)

Proof:

We know that in a parallelogram opposite sides are equal, that is

AD = BC and AB = CD

Now, consider ∆ABD and ∆BCD

Here AD = BC

AB = CD

BD = BD (common)

Hence by SSS congruency

∆ABD ∆BCD

By this we can conclude that both the triangles are equal

area(∆ABD) = area(∆BCD)

Hence proved

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